[2] In 1955 Andrei V. Roiter matriculated at Taras Shevchenko National University of Kyiv, where he met a fellow mathematics major Lyudmyla Nazarova.
[5] A. V. Roiter was hired in 1961 as a researcher at the Institute of Mathematics of the Academy of Sciences of Ukraine, where he worked until his death in 2006 and since 1991 was Head of the Department of Algebra.
[6] In his first published paper, Roiter in 1960[7] proved an important result that eventually led several other mathematicians to establish that a finite group
Rather, the research came from an effort to explain a much older result of Gabriel and Roiter ... concerning artin algebras of finite representation type in terms of the technics and ideas developed by Auslander and Reiten in connection with almost split sequences and irreducible morphisms ...[12]Roiter did important research on p-adic representations,[3] especially his 1967 paper with Yuriy Drozd and Vladimir V. Kirichenko on hereditary and Bass orders[14][15][16] and the Drozd-Roiter criterion for a commutative order to have finitely many non-isomorphic indecomposable representations.
[21]) Also in the 1970s Roiter in three papers, two of which were joint work with Mark Kleiner,[22][23][24][25] introduced representations of bocses, a very large class of matrix problems.
[29] In two papers,[30][31] he with his wife and Stanislav A. Kruglyak introduced the notion of locally scalar representations of quivers (i.e. directed multigraphs) in Hilbert spaces.
In 2007 A. V. Roiter was posthumously awarded the State Prize of Ukraine in Science and Technology for his research on representation theory.